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Home/Chain Registry/Block #3,457,899

Block #3,457,899

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/2/2019, 7:11:02 AM Β· Difficulty 10.9787 Β· 3,387,749 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
3172582cd58b7c1ef19518dcb7abe6862366b9fcb943df4217be767cb3043e82
View on Chainz β†—

Difficulty

10.978673

Transactions

1

Size

200 B

Version

2

Bits

0afa8a4f

Nonce

623,507,323

Timestamp

12/2/2019, 7:11:02 AM

Confirmations

3,387,749

Merkle Root

f8e9337320e714d3dd9f34e7529dc372cc257cf6e543bace1c8c8cee5c82845e
Transactions (1)
Coinbasef8e9337320e714…8c8cee5c82845e
1 in β†’ 1 out8.2800 XPM110 B
ASiq2qtK…VMhmk7yL
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

9.573 Γ— 10⁹⁴(95-digit number)
95732211430149035248…78872819133676410880
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
9.573 Γ— 10⁹⁴(95-digit number)
95732211430149035248…78872819133676410881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.914 Γ— 10⁹⁡(96-digit number)
19146442286029807049…57745638267352821761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.829 Γ— 10⁹⁡(96-digit number)
38292884572059614099…15491276534705643521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.658 Γ— 10⁹⁡(96-digit number)
76585769144119228198…30982553069411287041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.531 Γ— 10⁹⁢(97-digit number)
15317153828823845639…61965106138822574081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.063 Γ— 10⁹⁢(97-digit number)
30634307657647691279…23930212277645148161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.126 Γ— 10⁹⁢(97-digit number)
61268615315295382558…47860424555290296321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.225 Γ— 10⁹⁷(98-digit number)
12253723063059076511…95720849110580592641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.450 Γ— 10⁹⁷(98-digit number)
24507446126118153023…91441698221161185281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.901 Γ— 10⁹⁷(98-digit number)
49014892252236306047…82883396442322370561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.802 Γ— 10⁹⁷(98-digit number)
98029784504472612094…65766792884644741121
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 3457899

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 3172582cd58b7c1ef19518dcb7abe6862366b9fcb943df4217be767cb3043e82

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #3,457,899 on Chainz β†—
Circulating Supply:58,009,633 XPMΒ·at block #6,845,647 Β· updates every 60s
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